MATH118 final exam and answers 2006 - MATH 118 FINAL EXAM SPRING 2006 1 Short Answer Problems a What is the power series representation and radius of

MATH118 final exam and answers 2006 - MATH 118 FINAL EXAM...

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MATH 118 FINAL EXAM SPRING 2006 1.Short Answer Problemsa) What is the power series representation and radius of convergence forf(x) =11-x?b) Write the formula fordydxfor a parametric curvex(t),y(t).c) Write the definition of a Taylor series for a functionf(x) abouta.d) For what values ofpdoes the seriesn=11npconverge?2.Evaluate the following integrals.(If the integral is improper, state whether itconverges or diverges)a)2xe-x2dxb)1(x-1)(x-2)dxc)16-x2dxd)32x(x2-4)3/2dx3.Consider the curver= sinθ+ cosθ.a) Draw the curve on the axis. Show all steps used to arrive at your graph.b) Find the slope of the tangent line to the curve at the point(2,π4)4.Find the limit of the following sequences.a)an=n2+n-nb)b1= 1,bn+1=6 +bn5.Determine if the following series converge or diverge.a)n=0e-nb)n=1(-1)nn(n+1)c)n=2lnnn2d)n=011+100-n6.Determine the interval and radius of convergence ofn=11n(x+ 2)n.
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